Question

25 a summer camp hosts 500 campers. a random survey of 50 campers was conducted to determine which activity was their favorite. the table shows the number of campers who chose each activity. summer camp activities activity number of campers swimming 16 rock climbing 8 hiking 12 kayaking 14 based on the survey results, which of these is the best prediction about the favorite activities of the 500 campers? a there are 22 more campers who prefer kayaking than prefer rock climbing. b there are 8 more campers who prefer swimming than prefer rock climbing. c there are 20 more campers who prefer hiking than prefer kayaking. d there are 40 more campers who prefer swimming than prefer hiking.

Explanation:

Step1: Find the ratio of survey to total campers

The survey has 50 campers, and the total is 500. The ratio is $\frac{500}{50} = 10$. So we'll multiply each survey count by 10 to predict for 500 campers.

Step2: Analyze Option A

For kayaking: $14\times10 = 140$. For rock climbing: $8\times10 = 80$. Difference: $140 - 80 = 60
eq 22$. So A is wrong.

Step3: Analyze Option B

For swimming: $16\times10 = 160$. For rock climbing: $8\times10 = 80$. Difference: $160 - 80 = 80
eq 8$. Wait, no—wait, maybe I misread. Wait, the option B says "8 more" in the survey? Wait no, the question is about predicting for 500. Wait, no, maybe the options are about the survey scaled? Wait, no, let's recheck. Wait, the survey is 50, total is 500, so scale factor is 10. Wait, but option B: swimming in survey is 16, rock climbing 8. 16 - 8 = 8. Then scaled by 10? No, wait, the option B says "There are 8 more campers who prefer swimming than prefer rock climbing." Wait, in the survey, 16 - 8 = 8. Then when we scale to 500, the difference would be 8*10 = 80? Wait, no, maybe the options are written incorrectly, or I misinterpret. Wait, no—wait, the problem is: "which of these is the best prediction about the favorite activities of the 500 campers?" So we need to calculate the difference for 500. Wait, but let's check each option:

Option A: Kayaking (14) vs rock climbing (8) in survey. Difference in survey: 14 - 8 = 6. Scaled to 500: 6*10 = 60. But option A says 22. Wrong.

Option B: Swimming (16) vs rock climbing (8) in survey. Difference: 16 - 8 = 8. Scaled to 500: 810 = 80? Wait, no, maybe the option is about the survey? No, the question is about predicting for 500. Wait, maybe the options have a typo, or I'm misunderstanding. Wait, no—wait, the option B says "There are 8 more campers who prefer swimming than prefer rock climbing." If we take the survey numbers (16 and 8), 16 - 8 = 8. Then when we scale to 500, the difference would be 8(500/50) = 810 = 80. But the option says "8 more"—that doesn't match. Wait, maybe the options are not scaled? That can't be. Wait, no, maybe I made a mistake. Wait, let's check option D: swimming (16) vs hiking (12). Survey difference: 16 - 12 = 4. Scaled: 410 = 40. Oh! Option D says "There are 40 more campers who prefer swimming than prefer hiking." Let's check:

Swimming in 500: 16(500/50) = 160. Hiking: 12(500/50) = 120. 160 - 120 = 40. So D is correct. Wait, but earlier I thought B. Wait, let's recheck:

Option B: Swimming (16) vs rock climbing (8). 16 - 8 = 8 in survey. Scaled: 810 = 80. But option B says "8 more"—so that's wrong. Option D: swimming (16) vs hiking (12). 16 - 12 = 4 in survey. Scaled: 410 = 40. So option D says "40 more"—which matches. So D is correct. Wait, but let's re-express:

For each activity, number in 500 is (number in survey) (500/50) = (number in survey)10.

Swimming: 16*10=160

Rock climbing:8*10=80

Hiking:12*10=120

Kayaking:14*10=140

Now check each option:

A: Kayaking (140) - Rock climbing (80) = 60 ≠22 → wrong.

B: Swimming (160) - Rock climbing (80)=80≠8 → wrong.

C: Hiking (120) - Kayaking (140)= -20≠20 → wrong (and it says "20 more" for hiking than kayaking, but it's less).

D: Swimming (160) - Hiking (120)=40 → matches the option D: "There are 40 more campers who prefer swimming than prefer hiking." So D is correct.

Wait, but earlier I thought B, but that was a mistake. So the correct answer is D.

Answer:

D. There are 40 more campers who prefer swimming than prefer hiking.